Two- and four-dimensional representations of the PT- and CPT -symmetric fermionic algebras

• Verfasst von: Beygi, Alireza [VerfasserIn]
• Verfasst von: Klevansky, Sandra Pamela [VerfasserIn]
• Verfasst von: Bender, Carl M. [VerfasserIn]
• Titel: Two- and four-dimensional representations of the PT- and CPT -symmetric fermionic algebras
• Verf.angabe: Alireza Beygi, S.P. Klevansky, and Carl M. Bender
• E-Jahr: 2018
• Jahr: 28 March 2018
• Umfang: 6 S.
• Fussnoten: Gesehen am 05.11.2020
• Titel Quelle: Enthalten in: Physical review
• Ort Quelle: Woodbury, NY : Inst., 2016
• Jahr Quelle: 2018
• Band/Heft Quelle: 97(2018,3) Artikel-Nummer 032128, 6 Seiten
• ISSN Quelle: 2469-9934
• DOI: doi:10.1103/PhysRevA.97.032128
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1586408623

Abstract

Fermionic systems differ from their bosonic counterparts, the main difference with regard to symmetry considerations being that T2=−1 for fermionic systems. In PT-symmetric quantum mechanics an operator has both PT and CPT adjoints. Fermionic operators η, which are quadratically nilpotent (η2=0), and algebras with PT and CPT adjoints can be constructed. These algebras obey different anticommutation relations: ηηPT+ηPTη=−1, where ηPT is the PT adjoint of η, and ηηCPT+ηCPTη=1, where ηCPT is the CPT adjoint of η. This paper presents matrix representations for the operator η and its PT and CPT adjoints in two and four dimensions. A PT-symmetric second-quantized Hamiltonian modeled on quantum electrodynamics that describes a system of interacting fermions and bosons is constructed within this framework and is solved exactly.